Seminar on Qualitative Theory of Differential Equations - Pavol Quittner (11.4.2019)
Thursday 11.4.2019 at 14:00, Lecture room M/223
Pavol Quittner:
Entire solutions of a semilinear heat equation
Abstract:
We characterize some classes of positive entire solutions of the nonlinear heat equation $u_t=\Delta u+u^p$, where $p$ is supercritical in the Sobolev sense. In particular, if $p>p_L$ where $p_L$ denotes the Lepin exponent, then any positive entire radial solution has to be a steady state (the condition $p\geq p_L$ is known to be necessary for such statement). As an application, we show the convergence of rescaled profiles of solutions with type II blow-up and of global solutions with slow time decay.
This is a joint work with Peter Poláčik (University of Minnesota).